Two players, A and B, alternately and independently flip a biased coin and the first player to get a head wins. Assume player A flips first. Player A wins the game 12/23 times. If the coin is biased, what is the bias of the coin?
I am using the format from here Two players alternately flip a coin; what is the probability of winning by getting a head? except my equation looks 12/23 = p + (1-p)(11/23) and solving for p. I am getting p = 1/12.
I am not understanding the answer or if it is correct. If player A is more likely to win and has first flip, why is the chance of getting heads 1/12??